"""
Enhanced solver auto-selection based on PDE characteristics

This module provides intelligent solver selection based on PDE type,
problem characteristics, and performance requirements.
"""

using ..PDEs
using DifferentialEquations
using OrdinaryDiffEq

"""
    PDECharacteristics

Structure to hold analyzed PDE characteristics for solver selection.
"""
struct PDECharacteristics
    is_stiff::Bool
    is_nonlinear::Bool
    is_hyperbolic::Bool
    has_conservation_laws::Bool
    has_noise::Bool
    requires_high_accuracy::Bool
    requires_cfl_stability::Bool
    time_scale_ratio::Float64
    spatial_scale_ratio::Float64
    problem_size::Int
    
    function PDECharacteristics(pde::AbstractPDE, initial_state, grid_info=nothing)
        # Analyze PDE characteristics
        stiff = analyze_stiffness(pde, initial_state)
        nonlinear = analyze_nonlinearity(pde)
        hyperbolic = analyze_hyperbolicity(pde)
        conservation = analyze_conservation_laws(pde)
        noise = analyze_noise(pde)
        accuracy = analyze_accuracy_requirements(pde)
        cfl = analyze_cfl_requirements(pde)
        
        # Analyze time and spatial scales
        time_ratio = analyze_time_scales(pde, initial_state)
        spatial_ratio = analyze_spatial_scales(pde, initial_state)
        
        # Problem size
        size = get_problem_size(initial_state)
        
        new(stiff, nonlinear, hyperbolic, conservation, noise, accuracy, cfl,
            time_ratio, spatial_ratio, size)
    end
end

"""
    analyze_stiffness(pde::AbstractPDE, initial_state)

Analyze if the PDE is stiff based on type and parameters.
"""
function analyze_stiffness(pde::AbstractPDE, initial_state)
    # Check if PDE type is inherently stiff
    if isa(pde, CahnHilliardPDE) || isa(pde, KuramotoSivashinskyPDE) || 
       isa(pde, SwiftHohenbergPDE)
        return true
    end
    
    # Check for high-order derivatives
    if has_fourth_order_derivatives(pde)
        return true
    end
    
    # Check for small parameters that cause stiffness
    if has_small_parameters(pde)
        return true
    end
    
    # Default analysis based on diffusion coefficient
    if isa(pde, DiffusionPDE) && pde.diffusivity > 1.0
        return true
    end
    
    return false
end

"""
    analyze_nonlinearity(pde::AbstractPDE)

Check if PDE has nonlinear terms.
"""
function analyze_nonlinearity(pde::AbstractPDE)
    # Explicitly nonlinear PDEs
    if isa(pde, AllenCahnPDE) || isa(pde, CahnHilliardPDE) || 
       isa(pde, KPZInterfacePDE) || isa(pde, KuramotoSivashinskyPDE) ||
       isa(pde, SwiftHohenbergPDE) || isa(pde, ReactionDiffusionPDE)
        return true
    end
    
    # Check for nonlinear functions in generic PDEs
    if isa(pde, MultiFieldPDE)
        return true  # Assume nonlinear for generic systems
    end
    
    return false
end

"""
    analyze_hyperbolicity(pde::AbstractPDE)

Check if PDE is hyperbolic (wave-like).
"""
function analyze_hyperbolicity(pde::AbstractPDE)
    return isa(pde, WavePDE)
end

"""
    analyze_conservation_laws(pde::AbstractPDE)

Check if PDE has conservation laws.
"""
function analyze_conservation_laws(pde::AbstractPDE)
    # Mass-conserving PDEs
    if isa(pde, CahnHilliardPDE) || isa(pde, ReactionDiffusionPDE)
        return true
    end
    
    # Energy-conserving PDEs
    if isa(pde, WavePDE)
        return true
    end
    
    return false
end

"""
    analyze_noise(pde::AbstractPDE)

Check if PDE has stochastic terms.
"""
function analyze_noise(pde::AbstractPDE)
    if isa(pde, StochasticPDE)
        return true
    end
    
    if isa(pde, KPZInterfacePDE) && pde.noise > 0
        return true
    end
    
    if isa(pde, KuramotoSivashinskyPDE) && pde.noise > 0
        return true
    end
    
    return false
end

"""
    analyze_accuracy_requirements(pde::AbstractPDE)

Determine if PDE requires high accuracy solvers.
"""
function analyze_accuracy_requirements(pde::AbstractPDE)
    # Pattern-forming systems near bifurcations
    if isa(pde, SwiftHohenbergPDE) && abs(pde.rate) < 0.1
        return true
    end
    
    # Chaotic systems
    if isa(pde, KuramotoSivashinskyPDE)
        return true
    end
    
    # Interface dynamics
    if isa(pde, AllenCahnPDE) || isa(pde, CahnHilliardPDE)
        return true
    end
    
    return false
end

"""
    analyze_cfl_requirements(pde::AbstractPDE)

Check if PDE requires CFL stability condition.
"""
function analyze_cfl_requirements(pde::AbstractPDE)
    # Hyperbolic PDEs always need CFL
    if isa(pde, WavePDE)
        return true
    end
    
    # Advection-dominated problems
    # (Would need to check for advection terms)
    
    return false
end

"""
    analyze_time_scales(pde::AbstractPDE, initial_state)

Analyze ratio of time scales in the problem.
"""
function analyze_time_scales(pde::AbstractPDE, initial_state)
    # Estimate fastest and slowest time scales
    if isa(pde, CahnHilliardPDE) || isa(pde, KuramotoSivashinskyPDE)
        return 1000.0  # High ratio indicates multiple time scales
    end
    
    if isa(pde, SwiftHohenbergPDE) && abs(pde.rate) < 0.01
        return 100.0   # Near bifurcation has slow modes
    end
    
    return 1.0  # Default single time scale
end

"""
    analyze_spatial_scales(pde::AbstractPDE, initial_state)

Analyze ratio of spatial scales in the problem.
"""
function analyze_spatial_scales(pde::AbstractPDE, initial_state)
    # Interface problems have multiple scales
    if isa(pde, AllenCahnPDE) || isa(pde, CahnHilliardPDE)
        interface_width = get_interface_width(pde)
        # Domain size / interface width
        return 10.0  # Simplified estimate
    end
    
    return 1.0  # Default single spatial scale
end

"""
    get_problem_size(initial_state)

Get the problem size (number of degrees of freedom).
"""
function get_problem_size(initial_state)
    if isa(initial_state, ScalarField)
        return length(data(initial_state))
    elseif isa(initial_state, FieldCollection)
        total = 0
        for field in initial_state
            total += length(data(field))
        end
        return total
    else
        return 1000  # Default estimate
    end
end

"""
    has_fourth_order_derivatives(pde::AbstractPDE)

Check if PDE contains fourth-order derivatives.
"""
function has_fourth_order_derivatives(pde::AbstractPDE)
    return isa(pde, CahnHilliardPDE) || isa(pde, KuramotoSivashinskyPDE) || 
           isa(pde, SwiftHohenbergPDE)
end

"""
    has_small_parameters(pde::AbstractPDE)

Check if PDE has small parameters causing stiffness.
"""
function has_small_parameters(pde::AbstractPDE)
    if isa(pde, AllenCahnPDE) && pde.interface_width < 0.1
        return true
    end
    
    if isa(pde, DiffusionPDE) && pde.diffusivity < 0.01
        return true
    end
    
    return false
end

"""
    select_optimal_solver(pde::AbstractPDE, initial_state, t_span; performance_target="balanced")

Select optimal solver based on PDE characteristics and performance requirements.

# Performance targets:
- "fast": Prioritize speed over accuracy
- "accurate": Prioritize accuracy over speed  
- "balanced": Balance speed and accuracy
- "robust": Prioritize stability and reliability
"""
function select_optimal_solver(pde::AbstractPDE, initial_state, t_span; 
                              performance_target="balanced", tolerance=1e-6)
    
    characteristics = PDECharacteristics(pde, initial_state)
    
    # Select solver based on characteristics
    if characteristics.has_noise
        return select_stochastic_solver(characteristics, performance_target, tolerance)
    elseif characteristics.is_hyperbolic
        return select_hyperbolic_solver(characteristics, performance_target, tolerance)
    elseif characteristics.is_stiff
        return select_stiff_solver(characteristics, performance_target, tolerance)
    else
        return select_nonstiff_solver(characteristics, performance_target, tolerance)
    end
end

"""
    select_stochastic_solver(chars::PDECharacteristics, target, tol)

Select solver for stochastic PDEs.
"""
function select_stochastic_solver(chars::PDECharacteristics, target, tol)
    # For stochastic PDEs, we typically need special SDE solvers
    if target == "accurate"
        return (solver_type="EM", dt=0.001, adaptive=false)  # Euler-Maruyama
    elseif target == "fast"
        return (solver_type="EM", dt=0.01, adaptive=false)
    else
        return (solver_type="Milstein", dt=0.005, adaptive=false)  # Higher order
    end
end

"""
    select_hyperbolic_solver(chars::PDECharacteristics, target, tol)

Select solver for hyperbolic PDEs (wave equations).
"""
function select_hyperbolic_solver(chars::PDECharacteristics, target, tol)
    if target == "accurate"
        return (solver_type="SSPRK4", cfl=0.8, adaptive=true, reltol=tol)
    elseif target == "fast"
        return (solver_type="RK4", cfl=0.9, adaptive=false, reltol=tol*10)
    else
        return (solver_type="SSPRK3", cfl=0.85, adaptive=true, reltol=tol)
    end
end

"""
    select_stiff_solver(chars::PDECharacteristics, target, tol)

Select solver for stiff PDEs.
"""
function select_stiff_solver(chars::PDECharacteristics, target, tol)
    if chars.requires_high_accuracy || target == "accurate"
        if chars.problem_size > 10000
            return (solver_type="FBDF", reltol=tol, abstol=tol/100)  # For large systems
        else
            return (solver_type="Rodas5", reltol=tol, abstol=tol/100)  # High accuracy
        end
    elseif target == "fast"
        return (solver_type="ImplicitEuler", reltol=tol*10, abstol=tol)
    else
        if chars.problem_size > 5000
            return (solver_type="CVODE_BDF", reltol=tol, abstol=tol/10)
        else
            return (solver_type="Rodas4", reltol=tol, abstol=tol/10)
        end
    end
end

"""
    select_nonstiff_solver(chars::PDECharacteristics, target, tol)

Select solver for non-stiff PDEs.
"""
function select_nonstiff_solver(chars::PDECharacteristics, target, tol)
    if chars.requires_high_accuracy || target == "accurate"
        return (solver_type="Vern9", reltol=tol, abstol=tol/100, adaptive=true)
    elseif target == "fast"
        if chars.is_nonlinear
            return (solver_type="Tsit5", reltol=tol*10, abstol=tol, adaptive=true)
        else
            return (solver_type="RK4", dt=0.01, adaptive=false)
        end
    else
        if chars.is_nonlinear
            return (solver_type="Tsit5", reltol=tol, abstol=tol/10, adaptive=true)
        else
            return (solver_type="DP5", reltol=tol, abstol=tol/10, adaptive=true)
        end
    end
end

"""
    estimate_computational_cost(solver_config, problem_size, t_span)

Estimate computational cost for the selected solver configuration.
"""
function estimate_computational_cost(solver_config, problem_size, t_span)
    base_cost = problem_size * (t_span[2] - t_span[1])
    
    # Multiply by solver-specific factors
    if haskey(solver_config, :solver_type)
        solver_type = solver_config[:solver_type]
        if solver_type in ["FBDF", "CVODE_BDF", "Rodas5"]
            base_cost *= 5  # Implicit solvers are more expensive
        elseif solver_type in ["Vern9"]
            base_cost *= 3  # High-order methods
        elseif solver_type in ["RK4", "DP5"]
            base_cost *= 1  # Reference cost
        end
    end
    
    return base_cost
end

"""
    recommend_grid_resolution(pde::AbstractPDE, domain_size, accuracy_target="moderate")

Recommend grid resolution based on PDE characteristics.
"""
function recommend_grid_resolution(pde::AbstractPDE, domain_size, accuracy_target="moderate")
    if isa(pde, AllenCahnPDE) || isa(pde, CahnHilliardPDE)
        # Need to resolve interface width
        interface_width = get_interface_width(pde)
        points_per_interface = accuracy_target == "high" ? 8 : 4
        return ceil(Int, domain_size / (interface_width / points_per_interface))
        
    elseif isa(pde, KuramotoSivashinskyPDE)
        # Need fine resolution for chaotic dynamics
        return accuracy_target == "high" ? 256 : 128
        
    elseif isa(pde, SwiftHohenbergPDE)
        # Need to resolve critical wavelength
        critical_wavelength = get_critical_wavelength(pde)
        points_per_wavelength = accuracy_target == "high" ? 16 : 8
        return ceil(Int, domain_size / (critical_wavelength / points_per_wavelength))
        
    elseif isa(pde, WavePDE)
        # CFL condition determines minimum resolution
        return 64  # Default for wave problems
        
    else
        # Default recommendations
        if accuracy_target == "high"
            return 128
        elseif accuracy_target == "low"
            return 32
        else
            return 64
        end
    end
end

"""
    auto_solver(pde::AbstractPDE, initial_state, t_span=(0.0, 1.0); kwargs...)

Main interface for automatic solver selection.
"""
function auto_solver(pde::AbstractPDE, initial_state, t_span=(0.0, 1.0); 
                    performance_target="balanced", tolerance=1e-6, kwargs...)
    
    solver_config = select_optimal_solver(pde, initial_state, t_span; 
                                        performance_target=performance_target,
                                        tolerance=tolerance)
    
    # Create actual solver object based on configuration
    return create_solver_from_config(solver_config, kwargs...)
end

"""
    create_solver_from_config(config, kwargs...)

Create concrete solver object from configuration.
"""
function create_solver_from_config(config, kwargs...)
    # This would map configuration to actual solver constructors
    # Simplified for now - would need full implementation
    
    if haskey(config, :solver_type)
        solver_type = config[:solver_type]
        
        if solver_type == "Tsit5"
            return AdaptiveSolver(alg=Tsit5(), reltol=config[:reltol], 
                                abstol=config[:abstol]; kwargs...)
        elseif solver_type == "Rodas4"
            return AdaptiveSolver(alg=Rodas4(), reltol=config[:reltol],
                                abstol=config[:abstol]; kwargs...)
        elseif solver_type == "RK4"
            return RungeKuttaSolver(dt=get(config, :dt, 0.01); kwargs...)
        else
            # Default fallback
            return AdaptiveSolver(reltol=1e-6; kwargs...)
        end
    else
        return AdaptiveSolver(reltol=1e-6; kwargs...)
    end
end

# Export auto-selection functionality
export PDECharacteristics, select_optimal_solver, auto_solver
export recommend_grid_resolution, estimate_computational_cost